Question

The equation for line u can be written as y = -9/4x + 1. Line v, which is perpendicular to line u, includes the point (-3,2). What is the equation of line v?

Answer 1

To find the equation of a line perpendicular to another line, we need to find the negative reciprocal of the slope. The equation of line v, perpendicular to line u, is y = (4/9)x + 14/3.

Step-by-step explanation:

To find the equation of a line perpendicular to another line, we need to find the negative reciprocal of the slope. The given equation for line u is y = -9/4x + 1. The slope of line u is -9/4, so the slope of line v would be the negative reciprocal, which is 4/9. Using the point (-3,2), we can substitute the values into the point-slope formula y - y1 = m(x - x1) to find the equation of line v:

y - 2 = (4/9)(x + 3)

Expanding and simplifying the equation:

y - 2 = (4/9)x + 4/3

y = (4/9)x + 4/3 + 2

y = (4/9)x + 14/3